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What will be the total damage calculated if you used Muddy Water + Rain Dance?

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While Rain Dance is in effect, the base damage of Water-type moves will be increased by 50%, whereas the base damage of SolarBeam and Fire-type moves will be decreased by 50%. -Bulbapedia

Muddy Water's base power is 90. Half of 90 is 45. 90 + 45 = 135.

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Thank-you :)
Is accuracy also improved? with rain dance or no?
Rain doesn't increase the accuracies of anything. While thunder and hurricane are less likely to miss in rain, this technically counts as bypassing the accuracy check rather than increasing the accuracy.
If STAB is added, what will it be?
STAB is a 3/2 multiplier. 135 times 3/2 is 405/2, or 202.5.